few_shots: Example:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Mathematical concept/skill options: 
A. Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
B. Reason quantitatively and use units to solve problems.
C. Apply and extend previous understandings of numbers to the system of rational numbers.
D. Represent complex numbers and their operations on the complex plane.
E. Perform arithmetic operations with complex numbers.
F. Compute fluently with multi-digit numbers and find common factors and multiples.
G. Represent and model with vector quantities.
H. Perform operations on vectors.
I. Use properties of rational and irrational numbers.
J. Use complex numbers in polynomial identities and equations.
K. Extend the properties of exponents to rational exponents.
L. Know that there are numbers that are not rational, and approximate them by rational numbers.
M. Perform operations on matrices and use matrices in applications.
N. Apply and extend previous understandings of multiplication and division to divide fractions by fractions.


Thought: This problem involves understanding fractions, multiplication, and division.
Answer: A

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_001097

7
options: Perform operations with multi-digit whole numbers and with decimals to hundredths.

Extend the counting sequence.

Generalize place value understanding for multi-digit whole numbers.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.

Work with numbers 11–19 to gain foundations for place value.

Use place value understanding and properties of operations to add and subtract.

Understand place value.

Use place value understanding and properties of operations to perform multi-digit arithmetic. (A range of algorithms may be used.)

Use place value understanding and properties of operations to perform multi-digit arithmetic.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.

Understand the place value system.
problem_activity: Narrative
The purpose of this activity is for students to learn stage 5 of the Target Numbers center. Students subtract two-digit numbers to get as close to 0 as possible. For the introduction of this stage, invite students to count by 10 to 100 and represent their count with base-ten blocks. Then, they take turns rolling the 3 cubes to get a number to subtract. They choose one of the numbers on the cubes to represent the tens and a different number to represent the ones. Students subtract their tens and ones from the starting number. The difference becomes the first number in the next equation. The player who gets closest to 0 in 6 rounds, without going below 0, is the winner.
Required Materials
Materials to Gather
Base-ten blocks
Number cubes
Materials to Copy
Target Numbers Stage 5 Recording Sheet
Required Preparation
Each group of 2 students will need 3 number cubes.
Each group of 2 students will need base-ten blocks to represent at least 20 tens and 18 ones
.
Launch
Groups of 2
Give each student a copy of the recording sheet.
Give each group 3 number cubes and access to base-ten blocks.
“We are going to learn a new way to play Target Numbers. You and your partner will start with 100 and race to see who can reach a number less than 10 first.”
“Instead of using cards to decide whether to take away tens or ones, you will use number cubes to create a two-digit number and then subtract that number.”
“First, represent 100 with base-ten blocks."
As needed, invite students to count by 10 to 100 using the base-ten blocks or invite student to share how they might represent 100 with the blocks.
"When it’s your turn, roll all 3 number cubes. Pick 1 number to represent the tens and one number to represent the ones. Then show the subtraction with your blocks and write an equation on your recording sheet.”
“Take turns rolling and subtracting until the first person reaches a number less than 10.”
As needed, demonstrate a round with a student volunteer.
Activity
10
–
15 minutes: partner work
Activity Synthesis
Display equation:
\(73 - \underline{\hspace{1 cm}} = \underline{\hspace{1 cm}}\)
Draw or display number cubes showing 4, 2, and 5.
“What two-digit numbers could you create with this roll that would make you need to decompose a ten to subtract? How do you know?” (Sample response: 24 because if you subtract by place, there are only 3 ones, so you would need to decompose to take away 4 ones.)
“What two-digit numbers could you create that wouldn’t require decomposing a ten? How do you know?” (Sample response: 52 because if you subtract by place there are 3 ones and you can take away 2 ones from 3 ones.)
“What number would you create to try to get below 10 the fastest? Explain. (54 because it’s the number that lets you take away the most tens and ones.)


correct_option_index: 4